The objective of this study is to evaluate the safety and tolerability of multiple daily doses (once daily for 28 days) of FTY720 in stable renal transplant patients during steady-state administration of Neoral (cyclosporine) and prednisone. FTY720 is a potent immunosuppressive compound, which has been found to show synergistic effects on the prevention of rejection in animals when administered in combination with cyclosporine and tacrolimus. This is an ascending-dose, time-lagged and sequential group study. Stable renal allograft recipients who are at least 12 months posttransplant will be screened and enrolled in this 56-day study. Patients will receive FTY720 or placebo for 28 days and will be closely monitored during treatment and for 28 days after treatment has finished. Pharmacokinetics of both cyclosporine and FTY720 will be obtained at the start and end of treatment and trough levels of both drugs will be obtained throughout the study. Patients will be hospitalized on the GCRC for 5 days during the study and will have 21 outpatient visits scheduled during the study. Physical exams and safety laboratory assessments will be performed at each visit.